Maximum intersection of spherical polygons and workpiece orientation for 4- and 5-axis machining

Kai Tang; Tony Woo; Jacob Gan

Maximum intersection of spherical polygons and workpiece orientation for 4- and 5-axis machining

Kai Tang^*, Tony Woo, Jacob Gan

^*Corresponding author for this work

Research output: Contribution to conference › Conference Paper › peer-review

5 Citations (Scopus)

Abstract

Orienting the workpiece in such a way as to minimize the number of setups in a 4-axis or a 5-axis Numerical Control (NC) machine is formulated as follows: Given a set of spherical polygons (that are representations of curved surfaces visible to a 3-axis NC machine), find a great circle (the 4th axis) or a band (the 4th and the 5th axis) containing a great circle that intersects the polygons maximally. While there are potentially infinitely many solutions to this problem, a sphere is partitioned into O(N²) regions based on the N polygons. Within each of these regions, it is shown that it requires O(NlogN) time to determine maximum intersections and all the solutions are congruent. Central projection mapping is employed so as to present the algorithms in the plane.

Original language	English
Pages	183-192
Number of pages	10
Publication status	Published - 1990
Externally published	Yes
Event	1990 ASME Design Technical Conferences - Presented at the 16th Design Automation Conference - Chicago, IL, USA Duration: 16 Sept 1990 → 19 Sept 1990

Conference

Conference	1990 ASME Design Technical Conferences - Presented at the 16th Design Automation Conference
City	Chicago, IL, USA
Period	16/09/90 → 19/09/90

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Cite this

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title = "Maximum intersection of spherical polygons and workpiece orientation for 4- and 5-axis machining",

abstract = "Orienting the workpiece in such a way as to minimize the number of setups in a 4-axis or a 5-axis Numerical Control (NC) machine is formulated as follows: Given a set of spherical polygons (that are representations of curved surfaces visible to a 3-axis NC machine), find a great circle (the 4th axis) or a band (the 4th and the 5th axis) containing a great circle that intersects the polygons maximally. While there are potentially infinitely many solutions to this problem, a sphere is partitioned into O(N2) regions based on the N polygons. Within each of these regions, it is shown that it requires O(NlogN) time to determine maximum intersections and all the solutions are congruent. Central projection mapping is employed so as to present the algorithms in the plane.",

author = "Kai Tang and Tony Woo and Jacob Gan",

year = "1990",

language = "English",

pages = "183--192",

note = "1990 ASME Design Technical Conferences - Presented at the 16th Design Automation Conference ; Conference date: 16-09-1990 Through 19-09-1990",

}

TY - CONF

T1 - Maximum intersection of spherical polygons and workpiece orientation for 4- and 5-axis machining

AU - Tang, Kai

AU - Woo, Tony

AU - Gan, Jacob

PY - 1990

Y1 - 1990

N2 - Orienting the workpiece in such a way as to minimize the number of setups in a 4-axis or a 5-axis Numerical Control (NC) machine is formulated as follows: Given a set of spherical polygons (that are representations of curved surfaces visible to a 3-axis NC machine), find a great circle (the 4th axis) or a band (the 4th and the 5th axis) containing a great circle that intersects the polygons maximally. While there are potentially infinitely many solutions to this problem, a sphere is partitioned into O(N2) regions based on the N polygons. Within each of these regions, it is shown that it requires O(NlogN) time to determine maximum intersections and all the solutions are congruent. Central projection mapping is employed so as to present the algorithms in the plane.

AB - Orienting the workpiece in such a way as to minimize the number of setups in a 4-axis or a 5-axis Numerical Control (NC) machine is formulated as follows: Given a set of spherical polygons (that are representations of curved surfaces visible to a 3-axis NC machine), find a great circle (the 4th axis) or a band (the 4th and the 5th axis) containing a great circle that intersects the polygons maximally. While there are potentially infinitely many solutions to this problem, a sphere is partitioned into O(N2) regions based on the N polygons. Within each of these regions, it is shown that it requires O(NlogN) time to determine maximum intersections and all the solutions are congruent. Central projection mapping is employed so as to present the algorithms in the plane.

UR - http://www.scopus.com/inward/record.url?scp=0025533821&partnerID=8YFLogxK

M3 - Conference Paper

AN - SCOPUS:0025533821

SP - 183

EP - 192

T2 - 1990 ASME Design Technical Conferences - Presented at the 16th Design Automation Conference

Y2 - 16 September 1990 through 19 September 1990

ER -

Maximum intersection of spherical polygons and workpiece orientation for 4- and 5-axis machining

Abstract

Conference

UN SDGs

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